Graphing systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality. If it satisfies all inequalities, it is a solution.

Front

What does it mean when a graph is shaded above a line?

Back

It indicates that the solutions to the inequality are all the points above the line.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means greater than (not including the line), while '≥' means greater than or equal to (including the line).

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 as a dashed line and shade below it.

Front

What does the solution set of a system of inequalities represent?

Back

It represents all the points that satisfy all inequalities in the system.

Front

What is the significance of the boundary line in a graph of inequalities?

Back

The boundary line separates the solution region from the non-solution region.

Front

How do you identify the feasible region in a system of inequalities?

Back

The feasible region is the area where all shaded regions overlap.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If the inequality is '≥' or '≤', the point is included in the solution; if '>' or '<', it is not.

Front

How can you tell if a point is a solution to the inequality y ≥ -x + 1?

Back

Substitute the point into the inequality. If the inequality holds true, it is a solution.